Using the Factor Theorem to determine whether g(x) is a factor of p(x) in the following case (i) p(x) = 2x³+x²–2x–1, g(x) = x+1

Solution

p(x) = 2x³+x²–2x–1, g(x) = x+1
g(x) = 0
⇒ x+1 = 0
⇒ x = −1
∴Zero of g(x) is -1.
Now,
p(−1) = 2(−1)³+(−1)²–2(−1)–1
= −2+1+2−1
= 0
∴By the given factor theorem, g(x) is a factor of p(x).